Doors, coverings for various openings and other movable architectural elements are ubiquitous in residential, institutional, commercial, and industrial buildings. Moreover, doors take on a wide variety of sizes and configurations. For example, for doors that are powered opened or closed by a motor or other actuator, the following factors may be among those that are important for door operation: 1) reliability—such as having a simple construction and a minimum of moving parts; 2) opening/closing speed—a door that opens and closes rapidly can perform its function with a minimum air transfer through the doorway, and/or may enhance productivity in industrial or commercial settings; and 3) a minimal footprint—since space may be at a premium around a door opening, it is desirable for a door and its mounting structure and source of actuation to take up as little space as possible. A door, covering or other architectural element that addresses one or several of these factors, while providing other benefits and functionality, would be desirable.